The project (Delphi 7) I am working on has mushroomed from about 7 mByte to 13 mByte after initial passes through the units placing siLangLinked components. We have 4 languages defined (English, French, German and Spanish). I realize that when all translations are ready to go, we will create the SIL/SIB file and remove all translations. A smaller project that I did for a test case, however, still remained about 50% larger than before translation.

The size grow from 7 to 13 MB is very strange. Placing TsiLang on forms usually adds about 500 K to EXE. So I guess the origin of such growth might be somewhere else.
To create smaller EXE you can just export translations to SIB file and clear them in EXE right before the build. Additionally, I would recommend to check the translations list and be sure to remove items which don't need translations, since this will reduce size as well. Also using property AutoSkipEmpties = True will remove empty items significally reducing the size of translations.